Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 302 / 4 / e / Solution

The Fundamental representations of B2 have weight setsso $\dim d_{[1,0]}=4$, andso $\dim d_{[0,1]}=5$. The Adjoint representation has all eight roots as nonzero weights and zero with multiplicity two. Its highest root isso its highest-weight label is $[2,0]$ and its dimension is $8+2=10$.

Solved by gpt-5.6-sol high.